1. Field of the Invention
The present invention relates to a laser scanning optical system and an image forming apparatus using the same and, more particularly, to a laser scanning optical system suitable for an image forming apparatus such as a laser beam printer (LBP), a digital copying machine, or the like, which uses, e.g., an electrophotography process for recording image information by deflecting and reflecting a light beam (laser beam) emitted by a light source means comprising a semiconductor laser using-a light deflector comprising a rotary polygonal mirror (polygonal mirror), and then scanning the light beam on the surface to be scanned via a scanning lens system (f-.theta. lens) having f-.theta. characteristics.
2. Related Background Art
Conventionally, for example, as shown in Japanese Patent Application Laid-Open No. 3-231218, proposed a laser scanning optical system periodically deflects a light beam emitted by a light source means by a light deflector comprising, e.g., a rotary polygonal mirror, focusing the light beam into a spot shape on the surface of a photosensitive recording medium (photosensitive drum) via a scanning lens system, and scanning the light beam on that surface to record an image. FIGS. 1 and 2 are respectively a main scanning sectional view and a sub-scanning sectional view of the laser scanning optical system proposed by that reference.
In FIGS. 1 and 2, a light beam (laser beam) emitted by a light source means 101 comprising a semiconductor laser is converted into a nearly collimated light beam by a collimator lens 102, that light beam (light amount) is limited by a stop 103, and then enters a cylindrical lens 104 having a predetermined refractive power in only the sub-scanning section. The nearly collimated light beam that enters the cylindrical lens 104 leaves the cylindrical lens 104 in fact in the main scanning section. However, in the sub-scanning section, the nearly collimated light beam converges and forms a nearly line image on a deflection surface 105a of a light deflector 105 comprising a rotary polygonal mirror. The light beam deflected and reflected by the deflection surface 105a of the light deflector 105 is focused on the surface of a photosensitive drum 108 as the surface to be scanned via a scanning lens system (f-.theta. lens system) 111, which is comprised of a spherical lens 106 having a positive refractive power, and a toric lens (plastic toric lens) 107 formed of a plastic material having a positive refractive power in both the main scanning and sub-scanning directions. By rotating the light deflector 105 in the direction of an arrow A, the light beam scans, i.e., linearly moves at substantially equal velocity on the surface of the photosensitive drum 108 in the direction of an arrow B (main scanning direction), thus recording image information.
A numerical value example of the above-mentioned laser scanning optical system is listed below:
Focal length of scanning lens system: 188 mm PA1 Maximum scanning angle: 90.8.degree. PA1 Polygon center to R1 surface: 73.93 mm PA1 (for Y.gtoreq.0) EQU X=Y.sup.2 /RL[1+.sqroot.{1-(y/RL).sup.2 }]+B4LY.sup.4 +B6LY.sup.6 +B8LY.sup.8 +B10LY.sup.10 PA1 (for Y&lt;0) PA1 (for Y.gtoreq.0) EQU ru'=rL(1+D2LY.sup.2 +D4LY.sup.4 +D6LY.sup.6 +D8LY.sup.8 +D10LY.sup.10) PA1 (for Y&lt;0) PA1 the scanning lens system has a spherical lens, and a toric lens, which has a positive refractive power in both the main scanning and sub-scanning directions, and is formed of a plastic material, and PA1 at least one lens surface of the toric lens is formed by an aspherical shape which is substantially perpendicular to a light beam that is transmitted through the spherical lens in a main scanning section. PA1 the spherical lens has a positive refractive power, PA1 the spherical lens is formed of a glass material, and so forth. PA1 a ratio of the distance from a deflection point of the deflection means to the surface to be scanned to a focal length of the scanning lens system falls within a range from 1.34 to 1.2.
______________________________________ R1 = 988.25 D1 = 24 N1 = 1.51329 R2 = -135.8 D2 = 5 R3m = -1334.558 D3 = 7.5 N2 = 1.52179 R3s = -42.984 R4m = -347.830 D4 = 177.980 R4s = -20.740 ______________________________________
TABLE 1 __________________________________________________________________________ Table 1 below lists aspherical coefficients. 1 2 3 4 5 6 __________________________________________________________________________ Ru kyu B4u B6u B8u B10 -1.33456D+03 -7.31256D+02 -1.03710D-07 4.81636D-12 -4.38844D-16 0.00000D+00 R3m R1 B10 -1.33456D+03 -7.31256D+02 -1.03710D-07 4.81636D-12 -4.38844D-16 0.00000D+00 ru D10 -4.29835D+01 -6.57119D-05 1.76472D-08 -3.10098D-12 2.14963D-16 0.00000D+00 R3s r1 D10 -4.29835D+01 -5.70695D-05 9.39237D-09 -8.47573D-13 1.35957D-17 0.00000D+00 Ru B10 -3.47830D+02 9.08635D+00 0.00000D+00 0.00000D+00 0.00000D+00 0.00000D+00 R4m R1 B10 -3.47830D+02 9.08635D+00 0.00000D+00 0.00000D+00 0.00000D+00 0.00000D+00 ru D10 -2.07400D+01 0.00000D+00 0.00000D+00 0.00000D+00 0.00000D+00 0.00000D+00 R4s r1 D10 -2.07400D+01 0.00000D+00 0.00000D+00 0.00000D+00 0.00000D+00 0.00000D+00 __________________________________________________________________________
In the numerical value example, Ri is the paraxial radius of curvature of the i-th lens surface from the light deflector side, Di is the thickness and air gap of the i-th lens from the light deflector side, and Ni is the refractive index of the material of the i-th lens from the light deflector side. Also, m and s are suffices that respectively indicate the main scanning and sub-scanning directions. Furthermore, the light source wavelength is 675 nm, and the polygonal mirror is a hexahedron, which has a circumscribed circle diameter of 50 mm, and an incident deflection angle of 60.degree..
In Table-1, aspherical coefficients k, Bn, Dn of each order are expressed by relations of a generating line given by relations between the height y and distance x of the lens surface on an x-y plane:
Generating line: EQU X=Y.sup.2 /Ru[1+.sqroot.{1-(y/Ru).sup.2 }]+B4uY.sup.4 +B6uY.sup.6 +B8uY.sup.8 +B10uY.sup.10
and by relations of a meridian line given by the function of lens height:
Meridian line: EQU ru'=ru(1+D2uY.sup.2 +D4uY.sup.4 +D6uY.sup.6 +D8uY.sup.8 +D10uY.sup.10)
In the laser scanning optical system with such setups, let f2a be the focal length of the toric lens 107 in the main scanning section, and let fa be the focal length of the scanning lens system (synthesized one of the spherical lens 106 and toric lens 107) 111. Then, a laser scanning optical system which is excellent in wide field angle, high performance, size reduction, environmental-resistance-variation characteristics of a plastic lens, and cost can be realized by satisfying: EQU 0.1&lt;fa/f2a&lt;0.3 (1)
In the conventional laser scanning optical system, fa/f2a=0.21, which satisfies conditional formula (1) above.
However, when the lens surface of the toric lens uses a high-order aspherical surface, as described above, the toric lens must use plastic considering its manufacturing processes and cost. However, as is well known, since a plastic lens using a plastic material is weak against heat (environmental temperature) (i.e., its characteristics change considerably), coating is hard to attain. Also, since an increase in cost resulting from coating is larger than coating of a glass lens, a non-coating plastic lens is normally molded.
In general, when the incident angle of a light beam (light rays) on the lens surface changes depending on the scanning field angle, the Fresnel reflectance changes and the lens transmittance varies. For example, let .theta.i and .theta.o be the angles before and after the light beam is refracted at each lens surface. Then, the amplitude reflectances upon incidence of p-and s-polarized light beams (laser beams) coming from a semiconductor laser on the lens (optical element) are given by:
p-component amplitude reflectance: EQU Rp=tan(.theta.i-.theta.o)/tan(.theta.i+.theta.o) (2)
s-component amplitude reflectance: EQU Rs=sin(.theta.i-.theta.o)/sin(.theta.i+.theta.o) (3)
The Fresnel reflectance is obtained by calculating the squares of these equations (2) and (3).
Table-2(A) and Table-2(B) below respectively show the Fresnel reflectance of the conventional non-coating toric lens, and the variation ratio-in this Fresnel reflectance at each image height (distance from the scanning center on the surface 108 to be scanned) and at each field angle upon normalization, assuming that the on-axis reflectance is unity:
TABLE 2 __________________________________________________________________________ (A) Toric Lens Fresnel Reflectance of Prior Art Third Surface Fourth In case of In case of (deg) Surface (deg) p-polarized Laser s-polarized Laser Inci- Inci- Third Fourth Third Fourth Image Field dent Exit dent Exit Surface Surface Surface Surface Height Angle Angle Angle Angle Angle Reflec- Reflec- Reflec- Reflec- (mm) (deg) .theta.3i .theta.3o .theta.4i .theta.4o tance tance tance tance __________________________________________________________________________ -149.1 -45.4 -18.82 -12.24 -6.0 -9.1 0.037 0.041 0.049 0.044 -114.9 -35.0 -18.3 -11.9 -6.6 -10.1 0.037 0.041 0.049 0.045 0.0 0.0 0.3 0.2 0.4 0.5 0.043 0.043 0.043 0.043 114.9 35.0 18.5 12.0 6.7 10.3 0.037 0.041 0.049 0.045 149.1 45.4 18.2 11.8 5.5 8.4 0.037 0.042 0.049 0.044 __________________________________________________________________________ (B) Fresnel Reflectance Variation Ratio In case of In case of p-polarized Laser s-polarized Laser Third Fourth Third Fourth Image Field Surface Surface Surface Surface Height Angle Reflec- Reflec- Reflec- Reflec- (mm) (deg) tance tance tance tance __________________________________________________________________________ -149.1 -45.4 0.857 0.967 1.153 1.034 -114.9 -35.0 0.864 0.960 1.145 1.041 0.0 0.0 1.000 1.000 1.000 1.000 114.9 35.0 0.862 0.958 1.147 1.043 149.1 45.4 0.867 0.972 1.142 1.029 __________________________________________________________________________
As can be seen from Table-2(A) and Table-2(B), the Fresnel reflectance on the incident surface (third surface) changes with an increasing field angle, and the variation ratio in the entire scanning range reaches a maximum of approximately 15%. This produces an energy strength difference in a laser spot that scans the photosensitive drum surface, and the thickness and density of scanning lines at the central portion and two end portions of the scanning region change, thus causing the image to deteriorate.
As described above, in the conventional laser scanning optical system, when the incident angle of a light beam (light rays) on the lens surface changes depending on the scanning field angle, the Fresnel reflectance changes and the lens transmittance varies. As a result, it is hard to obtain a satisfactory image.
It is a common practice to use injection molding in the manufacture of an elongated toric lens consisting of a plastic material. The molding conditions upon injection molding roughly include parameters such as the temperature, pressure, cooling time, and the like. Hence, by optimizing these parameters, the molding conditions that can minimize birefringence and can make molding reproducibility most stable are determined.
However in injection molding, the setup lens shape largely influences its optical performance. That is, when the thickness of the lens in the optical axis direction changes in the longitudinal direction,
(1) the flow upon injecting a resin from a gate (entrance) at an end portion in the longitudinal direction becomes unstable, the resin cannot flow uniformly, and the molding parameters do not effect uniformly. For this reason, the optimal conditions of the parameters slightly vary in the longitudinal direction of the lens, the redundancies of the parameters that satisfy uniform optical performance are reduced, and the controllability and yield cannot be improved. Also, the optical performance deteriorates.
(2) When the variation in thickness is large, stress is locally concentrated in the cooling process, thus producing birefringence.
(3) Furthermore, when the central thickness becomes large, it is difficult to align the orientation axes of the resin, resulting in large birefringence. For this reason, conventionally, in order to assure the required thickness of the gate portion (end portion), a large central thickness must be inevitably set.
(4) Since the imaging spot on the surface to be scanned becomes large in a lens that suffers birefringence, if such lens is used in an image forming apparatus, fine image formation cannot be done, resulting in poor image quality.
FIGS. 3A and 3B are explanatory views showing the relationship between the lens height y and thickness in the conventional toric lens 107 shown in FIGS. 1 and 2. As shown in FIGS. 3A and 3B, the thickness at the most off-axis position (lens height=70 mm) is 3.5 mm while the central thickness is 7.5 mm; the thickness has changed approximately 55.6%.